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Simplifying 5x(x + -2) = 3x + 2 Reorder the terms: 5x(-2 + x) = 3x + 2 (-2 * 5x + x * 5x) = 3x + 2 (-10x + 5x2) = 3x + 2 Reorder the terms: -10x + 5x2 = 2 + 3x Solving -10x + 5x2 = 2 + 3x Solving for variable 'x'. Reorder the terms: -2 + -10x + -3x + 5x2 = 2 + 3x + -2 + -3x Combine like terms: -10x + -3x = -13x -2 + -13x + 5x2 = 2 + 3x + -2 + -3x Reorder the terms: -2 + -13x + 5x2 = 2 + -2 + 3x + -3x Combine like terms: 2 + -2 = 0 -2 + -13x + 5x2 = 0 + 3x + -3x -2 + -13x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -2 + -13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -2.6x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.6x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.6x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.6x + x2 = 0 + 0.4 -2.6x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.6x + x2 = 0.4 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = 0.4 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 0.4 + 1.69 Combine like terms: 0.4 + 1.69 = 2.09 1.69 + -2.6x + x2 = 2.09 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (x + -1.3) equal to 1.445683229 and -1.445683229.Subproblem 1
x + -1.3 = 1.445683229 Simplifying x + -1.3 = 1.445683229 Reorder the terms: -1.3 + x = 1.445683229 Solving -1.3 + x = 1.445683229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 1.445683229 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 1.445683229 + 1.3 x = 1.445683229 + 1.3 Combine like terms: 1.445683229 + 1.3 = 2.745683229 x = 2.745683229 Simplifying x = 2.745683229Subproblem 2
x + -1.3 = -1.445683229 Simplifying x + -1.3 = -1.445683229 Reorder the terms: -1.3 + x = -1.445683229 Solving -1.3 + x = -1.445683229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -1.445683229 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -1.445683229 + 1.3 x = -1.445683229 + 1.3 Combine like terms: -1.445683229 + 1.3 = -0.145683229 x = -0.145683229 Simplifying x = -0.145683229Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.745683229, -0.145683229}
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